Question

Find the large number which divides 245 and 1024 leaving remainder 5 in each case

Answer 1

Answer:

The two numbers are 245 and 1029. You want the largest number that divides the two numbers leaving a remainder of 5 in each case.

First subtract 5 from 245 and 1029 to get

245 - 5 = 240.

1029 - 5 = 1024,

Next find the HCF of 240 and 1024. To do that find the prime factors of the two numbers:

240 = 2x2x2x2x3x5 = 2^4x3x5

1024 = 2x2x2x2x2x2x2x2x2x2 = 2^10

Thus the HCF = 2^4 = 16. So the answer is 16.

Check: 245/16 = 30 + 5 remainder

1029/16 = 64+ 5 remainder

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